If, prove that,

.

Given,

To prove:

Note:

I. Sum of first n natural numbers, 1 + 2 +3+…n,

II. Sum of squares of first n natural numbers, 1² + 2² + 3²+….n²,

III. Sum of cubes of first n natural numbers, 1³ + 2³ + 3³ +…..n³,

IV. Sum of a constant k, N times,

So,

Now, the Left hand side of the condition given in the question can be written as,

The required LHS,

So,

_,

With,

Hence proved.